Asymptotic expansion and central limit theorem for multiscale piecewise-deterministic Markov processes

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• 作者：Khashayar Pakdaman^a ; ^{pakdaman@ijm.univ-paris-diderot.fr} ; Michè ; le Thieullen^b ; ^{michele.thieullen@upmc.fr} ; Gilles Wainrib^c ; ^{wainrib@math.univ-paris13.fr}
• 关键词：Piecewise-deterministic Markov process ; Averaging ; Homogenization ; Central limit theorem ; Multiscale ; Slow-fast ; Neuron models with stochastic ion channels
• 刊名：Stochastic Processes and their Applications
• 出版年：2012
• 出版时间：June, 2012
• 年：2012
• 卷：122
• 期：6
• 页码：2292-2318
• 全文大小：299 K

文摘

We consider a general class of piecewise-deterministic Markov processes with multiple time-scales. In line with recent results on the stochastic averaging principle for these processes, we obtain a description of their law through an asymptotic expansion. We further study the fluctuations around the averaged system in the form of a central limit theorem, and derive consequences on the law of the first passage-time. We apply the mathematical results to the Morris-Lecar model with stochastic ion channels.